Expansion — Set 4
Physics · प्रसार · Questions 31–40 of 40
A wire has α = 2×10^-5 K^-1 and is heated by 50 K. The fractional increase in length is?
Correct Answer: D. 1×10^-3
Fractional change in length equals αΔT. Here αΔT = 2×10^-5 × 50 = 1×10^-3. This means the length increases by 0.1%.
A 1.0 m steel rod has α = 12×10^-6 K^-1 and is heated by 100 K. The increase in length is approximately?
Correct Answer: D. 1.2 mm
Use ΔL = αLΔT for linear expansion. ΔL = 12×10^-6 × 1.0 × 100 = 12×10^-4 m. That equals 0.0012 m, which is 1.2 mm.
For small temperature changes, the area expansion of an isotropic solid is approximately given by?
Correct Answer: D. ΔA = 2αAΔT
Area expands in two perpendicular directions. For small expansions, fractional area change is about 2αΔT. So ΔA ≈ 2αAΔT is used.
The expression for cubical (volume) expansion of a solid is?
Correct Answer: B. ΔV = γVΔT
Volume expansion is proportional to original volume and temperature rise. The proportionality constant is the cubical expansion coefficient γ. Therefore ΔV = γVΔT.
If a liquid is heated in a container that also expands, the apparent expansion of the liquid will be?
Correct Answer: C. Less than real expansion
Real expansion is the true increase in liquid volume. The container also expands, increasing the container volume. So the observed apparent expansion becomes less than the real expansion.
A bimetallic thermometer works mainly due to?
Correct Answer: C. Bending due to different expansions of two metals
Two bonded metals expand by different amounts when heated. This mismatch produces bending of the strip. The bending is calibrated to indicate temperature.
Thermal strain in a freely expanding rod is given by?
Correct Answer: A. ΔL/L = αΔT
Thermal strain is the fractional change in length. For free expansion, ΔL = αLΔT, so ΔL/L = αΔT. This shows strain depends only on α and the temperature change.
The coefficient of volume expansion of an ideal gas at constant pressure is approximately?
Correct Answer: D. 1/273 per °C near 0°C
At constant pressure, V is proportional to absolute temperature T. So the fractional change per degree is about 1/T. Near 0°C, T ≈ 273 K, giving about 1/273 per °C.
Water pipes can burst in very cold weather mainly because water?
Correct Answer: B. Expands on freezing
Water expands when it freezes into ice. This increase in volume can create high pressure inside a closed pipe. That pressure may crack or burst the pipe.
In a mercury-in-glass thermometer, the mercury level rises with temperature mainly because?
Correct Answer: C. Mercury expands more than the glass container
Both mercury and glass expand on heating, but mercury expands more. So the excess expansion pushes mercury up the capillary tube. This rise is calibrated to show temperature.